Veteran striker Davies headed home midway through the opening period for his first strike of the season, and it proved to be the winner to leave Coventry, after 18 visits, still searching for a league win at Preston.
The hosts took the lead with the first real chance in the 21st minute when Paul Gallagher’s floated cross was met by Davies, who headed over Coventry goalkeeper Lee Burge and into the net from eight yards.
Davies almost doubled his tally 13 minutes later when Gallagher’s cross evaded two defenders and was chested goalwards by the striker from close range but this time Burge managed to push it over the bar.
Frank Nouble should have equalised just before the hour mark as Luke Williams picked him out from the right but he skied over the bar from six yards.
Coventry built some second-half pressure and in injury-time John Fleck’s left-footed strike from 35 yards rattled off the frame of the goal, but the hosts held on for the three points.